Further Mathematics Past Questions and Answers

Evaluate \(\lim \limits_{x \to 3} \frac{x^{2} - 2x - 3}{x - 3}\)

If \(f(x) = mx^{2} - 6x - 3\) and \(f'(1) = 12\), find the value of the constant m.

A bag contains 2 red and 4 green sweets of the same size and shape. Two boys pick a sweet each from the box, one after the other, without replacement. What is the probability that at least a sweet with green wrapper is picked?

A body is acted upon by two forces \(F_{1} = (5 N, 060°)\) and \(F_{2} = (10 N, 180°)\). Find the magnitude of the resultant force.

The equation of a curve is given by \(y = 2x^{2} - 5x + k\). If the curve has two intercepts on the x- axis, find the value(s) of constant k.